If you want to, you can learn Bayesian probability theory. Start withJaynes, it shouldn’t take more than about ten years to finish the book,assuming you don’t waste time on anything else, making it excellent valuefor money. If you do, you will be acquiring the skill of thinking in anon-Aristotelian Logic, just as advertised. This will make it possible foryou to solve problems that are currently beyond your powers to even statelet alone solve. People who can reason in such a way about the world arereadily employable and useful members of society: we call themstatisticians.

I claimed that mastering a non-Aristotelian logic makes you smarter and ableto see things lesser mortals cannot. An example would help at this point;you can see a small problem though: if you are still a lesser mortal, howwill you see it? Still, I shall give one anyway; it deals with the expectedlifetime of the human species. Papers have been written explaining that itis very likely that the human race will be extinct within a few thousandyears. The argument is one which the simple minded non-Bayesian might findconvincing, but which the Bayesian super-mind can penetrate easily anddispose of as a pile of dingo-droppings. Naturally, since you are not, asyet, a Bayesian super-mind, you won’t follow this – but you may get theflavour of it.

Imagine that you are given a box which is fixed on a desk top and has abutton on top.

You are told that the box may contain either ten balls or a thousand balls.All the balls are the same except that one and only one has your nameprinted on it. You are asked to decide which box you have here, the thousandball box or the ten ball box. All you can do is to press the button, and youare told that when you do, a ball will fall out of the box.

You reason that you have to press the button eleven times. If the eleventhbutton press produces a ball, then it must have been the thousand ball box,since the ten ball box wouldn’t have anything to produce. So far we haveconventional Aristotelian type reasoning.

You press the button once and a ball comes out. You press it again andanother ball comes out. You press it again and a third ball comes out – andthis one has your name on it.

You can now make a pretty good guess as to which box you have. It is onehundred times as likely to be the ten ball box as the thousand ball box.This result should agree with your intuitions if you have any. The Bayesiancan provide a justification for this very quickly – but this is easy andunderstandable only for superbeings and you aren’t one yet. You should,however, be able to see that getting your name up in the first three goes isnot too improbable if there are only ten balls in the box but is awfullyunlikely if there are a thousand. And if it is a hundred times as unlikely,then the ten ball explanation ought to be about a hundred times asbelievable. This is the intuitive, common sense approach. To a Bayesian, itis not just plausible it is blindingly obvious – although it requires someadditional assumptions, which he or she can state precisely and you can’t.This is because as a result of using a powerful non-Aristotelian Logic, theyare smarter than you. Annoying, isn’t it?